Find an explicit formula for the arithmetic sequence $12, 5, -2, -9,...$. Note: the first term should be $\textit{a(1)}$. $a(n)=$
Solution: The general explicit formula for arithmetic sequences is ${a_1}+{d}(n-1)$, where ${a_1}$ is the first term and $ d$ is the common difference. The first term is ${12}$ and the common difference is ${-7}$. ${-7\,\curvearrowright}$ ${-7\,\curvearrowright}$ ${-7\,\curvearrowright}$ ${12},$ $5,$ $-2,$ $-9,...$ This is the explicit formula for the arithmetic sequence $12, 5, -2, -9,...$. $a(n)={12}{-7}(n-1)$ Note that this solution strategy results in this formula, however an equally correct solution can be written in other equivalent forms as well.